viz.,
1. Created a directory in my home directory called OpenFOAM
2. Downloaded and copied all the tarfiles to that directory
3. Untarred them in sequence, first with the source tars for
OpenFOAM and ThirdParty and then the binaries
4. Added the lines in my .cshrc file so that OpenFOAM's
etc/cshrc file is sourced.
5. Sourced my .cshrc
6. Typed foamInstallationTest to check the install.

I get the errors below, saying there are two critical
errors, one related to gcc and another related to icoFoam.

BTW, $FOAM_APPBIN is empty and $FOAM_LIBBIN has a
directory called openmpi-1.2.6 (I saw that this was asked of
someone who posted a query on this topic earlier ... but that
was with an earlier (1.4?) build of OpenFOAM).

Third party software
-------------------------------------------------------------------------------
Software Version Location
-------------------------------------------------------------------------------
WARNING: gcc version does not match gcc supplied with this release of OpenFOAM
Supplied version: 4.3.1
User version : 3.4.3
Minimum required: 4.2.0

I looked at some older posts and saw something that helped. Essentially, what the problem was is that the downloads create these directories called linux64... and those directories are empty. So I deleted them, and instead created a link so that those names pointed to the corresponding 32 bit versions of linux.

This made the foamInstallationTest work.

Three questions:
1. Is this a bug that needs to be fixed in future tarballs of OpenFOAM?
2. Is this just a patch-up solution or do I need
to do something better?
3. Right now, for starters, I am just using the
existing functionality. I am planning to do
source code modification for my specialized
applications when necessary. At that point I
will have to do the full compilation of the
code myself.
Will the modifications that I have done to get
things to work right now work later if I do this?

I have no idea how your modificaton worked even when the eror says that your gcc version is lower.
But if it's running dont bother. I fyou get errors in compilation then i suggest you copy linux 32 directory such that your gcc path in .cshrc will change from

ThirdParty/gcc-4.3.1/platforms/linux

to

ThirdParty/gcc-4.3.1/linux

(move required linux folder from platforms folder and bring it in gcc-4.3.1 folder)